New Approaches to Linear Gradient Elution Used for Optimization in Reversed-Phase Liquid Chromatography

REFERENCES

• Snyder , L.R. ; Glajch , J.L. ; Kirkland , J.J. Practical HPLC Method Development ; Chapter 8 ; Wiley-Interscience : New York , 1997 .
   Google Scholar
• Jandera , P. ; Churacek , J. Liquid chromatography with programmed composition of the mobile phase . Adv. Chromatogr. 1980 , 19 , 125 – 260 .
   Google Scholar
• Jandera , P. ; Churacek , J. Gradient Elution in Column Liquid Chromatography ; Elsevier : Amsterdam , 1985 .
   Google Scholar
• Snyder , L.R. ; Dolan , J.W. The linear-solvent-strength model of gradient elution . Adv. Chromatogr. 1998 , 38 , 115 – 187 .
   Web of Science ®Google Scholar
• Jandera , P. Gradient elution in liquid column chromatography-prediction of retention and optimization of separation . Adv. Chromatogr. 2005 , 43 , 1 – 108 .
   PubMed Web of Science ®Google Scholar
• Jandera , P. Can the theory of gradient liquid chromatography be useful in solving practical problems? J. Chromatogr. A. 2006 , 1126 , 195 – 218 .
   Google Scholar
• Viseras , C. ; Cela , R. ; Barroso , C.G. ; Perez-Bustamante , J.A. Influence of temperature in reverse-phase high-performance liquid chromatography with gradient elution . Anal. Chim. Acta. 1987 , 196 , 115 – 122 .
   Google Scholar
• Zhu , P.L. ; Dolan , J.W. ; Snyder , L.R. Combined use of temperature and solvent strength in reversed-phase gradient elution II. Comparing selectivity for different samples and systems . J. Chromatogr. A. 1996 , 756 , 41 – 50 .
   Web of Science ®Google Scholar
• Zhu , P.L. ; Dolan , J.W. ; Snyder , L.R. ; Hill , D.W. ; Van Heukelem , L. ; Waeghe , T.J. Combined use of temperature and solvent strength in reversed-phase gradient elution III. Selectivity for ionizable samples as a function of sample type and pH . J. Chromatogr. A. 1996 , 756 , 51 – 62 .
   Web of Science ®Google Scholar
• Zhu , P.L. ; Dolan , J.W. ; Snyder , L.R. ; Djordjevic , N.M. ; Hill , D.W. ; Lin , J.-T. ; Sander , L.C. ; Van Heukelem , L. Combined use of temperature and solvent strength in reversed-phase gradient elution IV. Selectivity for neutral (non-ionized) samples as a function of sample type and other separation conditions . J. Chromatogr. A. 1996 , 756 , 63 – 72 .
   Web of Science ®Google Scholar
• Zhu , P.L. ; Snyder , L.R. ; Dolan , J.W. ; Djordjevic , N.M. ; Hill , D.W. ; Sander , L.C. ; Waeghe , T.J. Combined use of temperature and solvent strength in reversed-phase gradient elution I. Predicting separation as a function of temperature and gradient conditions. J. Chromatogr. A. 1996, 756, 21–39.
   PubMed Web of Science ®Google Scholar
• Pappa-Louisi , A. ; Nikitas , P. ; Zisi , C. ; Papachristos , K. Combined effect of temperature and organic modifier concentration on the retention under one mode gradient conditions in reversed-phase liquid chromatography . J. Sep. Sci. , 2008 , 31 , 2953 – 2961 .
   Google Scholar
• Bidlingmayer , B. ; Unger , K.K. ; von Doehren , N. Comparative study on the column performance of microparticulate 5-µm C18-bonded and monolithic C18-bonded reversed-phase columns in high-performance liquid chromatography . J. Chromatogr. A. 1999 , 832 , 11 – 16 .
   Google Scholar
• Lesins , V. ; Ruckenstein , E. Gradient flow programming: a coupling of gradient elution and flow programming . J. Chromatogr. 1989 , 467 , 1 – 14 .
   Google Scholar
• Nikitas , P. ; Pappa-Louisi , A. ; Balkatzopoulou , P. Theory of stepwise gradient elution in reversed-phase liquid chromatography coupled with flow rate variations: Application to retention prediction and separation optimization of a set of amino acids . Anal. Chem. 2006 , 78 , 5774 – 5782 .
   PubMedGoogle Scholar
• Pappa-Louisi , A. ; Nikitas , P. ; Balkatzopoulou , P. ; Louizis , G. Fundamental equation of dual-mode gradient elution in liquid chromatography involving simultaneous changes in flow rate and mobile-phase composition . Anal. Chem. 2007 , 79 , 3888 – 3893 .
   PubMed Web of Science ®Google Scholar
• Nikitas , P. ; Pappa-Louisi , A. ; Papachristos , K. ; Zisi , C. Theory and application of the two-mode gradient elution in liquid chromatography involving simultaneous changes in temperature and mobile-phase composition . Anal. Chem. 2008 , 80 , 5508 – 5514 .
   Google Scholar
• Snyder , L.R. ; Dolan , J.W. ; Gant , J.R. Gradient elution in high-performance liquid chromatography: I. Theoretical basis for reversed-phase systems . J. Chromatogr. 1979 , 165 , 1 – 30 .
   Google Scholar
• Snyder , L.R. ; Dolan , J.W. ; Gant , J.R. Gradient elution in high-performance liquid chromatography: II. Practical application to reversed-phase systems . J. Chromatogr. 1979 , 165 , 31 – 58 .
   Web of Science ®Google Scholar
• Snyder , L.R. ; Stadalious , M.A. ; Quarry , M.A. Gradient elution in reversed-phase HPLC-separation of macromolecules . Anal. Chem. 1983 , 55 , 1412A – 1430A .
   Google Scholar
• Dolan , J.W. ; Snyder , L.R. ; Quarry , M.A. Computer simulation as a means of developing an optimized reversed-phase gradient-elution separation . Chromatographia 1987 , 24 , 261 – 276 .
   Web of Science ®Google Scholar
• Ghrist , B.F.D. ; Coopermann , B.S. ; Snyder , L.R. Design of optimized high-performance liquid chromatographic gradients for the separation of either small or large molecules: I. Minimizing errors in computer simulations . J. Chromatogr. 1988 , 459 , 1 – 23 .
   PubMedGoogle Scholar
• Ghrist , B.F.D. ; Coopermann , B.S. ; Snyder , L.R. Design of optimized high-performance liquid chromatographic gradients for the separation of either small or large molecules: II. Background and theory . J. Chromatogr. 1988 , 459 , 25 – 41 .
   Google Scholar
• Ghrist , B.F.D. ; Coopermann , B.S. ; Snyder , L.R. Design of optimized high-performance liquid chromatographic gradients for the separation of either small or large molecules: III. An overall strategy and its application to several examples. J. Chromatogr. 1988, 459, 43–63.
   Google Scholar
• Snyder , L.R. ; Dolan , J.W. ; Lammen , D.C. Drylab® computer simulation for high-performance liquid chromatographic method development: I. Isocratic elution . J. Chromatogr. 1989 , 485 , 65 – 89 .
   Web of Science ®Google Scholar
• Dolan , J.W. ; Lammen , D.C. ; Snyder , L.R. Drylab® computer simulation for high-performance liquid chromatographic method development: II. Gradient Elution . J. Chromatogr. 1989 , 485 , 91 – 112 .
   PubMed Web of Science ®Google Scholar
• Molnar , I. Computerized design of separation strategies by reversed-phase liquid chromatography: development of DryLab software . J. Chromatogr. A. 2002 , 965 , 175 – 194 .
   PubMed Web of Science ®Google Scholar
• Cela , R. ; Lores , M. PREOPT-W: A simulation program for off-line optimization of binary gradient separations in HPLC—II. Data management and miscellaneous aspects of use . Comput. Chem. 1996 , 20 , 193 – 202 .
   Google Scholar
• Heinisch , S. ; Lesellier , E. ; Podevin , C. ; Rocca , J.L. ; Tchapla , A. Computerized optimization of RP-HPLC separation with nonaqueous or partially aqueous mobile phases . Chromatographia 1997 , 44 , 529 – 537 .
   Web of Science ®Google Scholar
• Torres-Lapasio , J.R. ; Garcιa-Alvarez-Coque , M.C. ; Baeza-Baeza , J.J. Global treatment of chromatographic data with MICHROM . Anal. Chim. Acta. 1997 , 348 , 187 – 196 .
   Web of Science ®Google Scholar
• Torres-Lapasio , J.R. MICHROM Software ; Marcel Dekker : New York , 2000 .
   Google Scholar
• Beinert , W.D. ; Jack , R. ; Eckert , V. ; Galushko , S. ; Tanchuck , V. ; Shishkina , I. A program for automated HPLC method development . Intl. Lab. 2001 , 31 , 16 – 27 .
   Google Scholar
• Nikitas , P. ; Pappa-Louisi , A. Expressions of the fundamental equation of gradient elution and a numerical solution of these equations under any gradient profile . Anal. Chem. 2005 , 77 , 5670 – 5677 .
   PubMedGoogle Scholar
• Snyder , L.R. Linear elution adsorption chromatography: VII. gradient elution theory . J. Chromatogr. 1964 , 13 , 415 – 434 .
   PubMed Web of Science ®Google Scholar
• Snyder , L.R. Principles of gradient elution . Chromatogr. Rev. 1965 , 7 , 1 – 51 .
   PubMedGoogle Scholar
• Snyder , L.R. ; Saunders , D.L. Optimized solvent programming for separations of complex samples by liquid-solid adsorption chromatography in columns . J. Chromatogr. Sci. 1969 , 7 , 145 – 159 .
   Google Scholar
• Snyder , L.R. in High Performance Liquid Chromatography ; Horvath , C. , Ed.; Academic Press : New York , 1980 ; Vol. 1 , 207 .
   Google Scholar
• Quarry , M.A. ; Grob , R.L. ; Snyder , L.R. Prediction of precise isocratic retention data from two or more gradient elution runs. Analysis of some associated errors . Anal. Chem. 1986 , 58 , 907 – 917 .
   Web of Science ®Google Scholar
• Pappa-Louisi , A. ; Nikitas , P. ; Zitrou , A. Modelling flow rate gradient elution in reversed-phase liquid chromatography . Anal. Chim. Acta. 2006 , 573 , 305 – 310 .
   Google Scholar
• Poole , C.F. The Essence of Chromatography ; Elsevier : Amsterdam , 2003 .
   Google Scholar
• Valko , K. ; Snyder , L.R. ; Glajch , J.L. Retention in reversed-phase liquid chromatography as a function of mobile-phase composition . J. Chromatogr. A. 1993 , 656 , 501 – 520 .
   Web of Science ®Google Scholar
• Schoenmakers , P.J. ; Billiet , H.A.H. ; Tijssen , R. ; de Galan , L. Gradient selection in reversed-phase liquid chromatography. J. Chromatogr. 1978, 149, 519–537.
   Web of Science ®Google Scholar
• Schoenmakers , P.J. ; Biliiet , H.A.H. ; de Galan , L. Description of solute retention over the full range of mobile phase compositions in reversed-phase liquid chromatography . J. Chromatogr. 1983 , 282 , 107 – 121 .
   Web of Science ®Google Scholar
• Schoenmakers , P.J. ; Billiet , H.A.H. ; de Galan , L. The solubility parameter as a tool in understanding liquid chromatography . Chromatographia 1982 , 15 , 205 – 214 .
   Web of Science ®Google Scholar
• Nikitas , P. ; Pappa-Louisi , A. ; Agrafiotou , P. Effect of the organic modifier concentration on the retention in reversed-phase liquid chromatography: II. Tests using various simplified models . J. Chromatogr. A. 2002 , 946 , 33 – 45 .
   PubMed Web of Science ®Google Scholar
• Pappa-Louisi , A. ; Nikitas , P. ; Balkatzopoulou , P. ; Malliakas , C. Two- and three-parameter equations for representation of retention data in reversed-phase liquid chromatography . J. Chromatogr. A. 2004 , 1033 , 29 – 41 .
   Google Scholar
• Neue , U.D. ; Phoebe , C.H. ; Tran , K. ; Cheng , Y.-F. ; Lu , Z. Dependence of reversed-phase retention of ionizable analytes on pH, concentration of organic solvent and silanol activity . J. Chromatogr. A. 2001 , 925 , 49 – 67 .
   PubMed Web of Science ®Google Scholar
• Pappa-Louisi , A. ; Nikitas , P. ; Papachristos , K. ; Zisi , C. Modeling the combined effect of temperature and organic modifier content on reversed-phase chromatographic retention: Effectiveness of derived models in isocratic and isothermal mode retention prediction . J. Chromatogr. A. 2008 , 1201 , 27 – 34 .
   Google Scholar
• Wolcott , R.G. ; Dolan , J.W. ; Snyder , L.R. Computer simulation for the convenient optimization of isocratic reversed-phase liquid chromatographic separations by varying temperature and mobile phase strength . J. Chromatogr. A. 2000 , 869 , 3 – 25 .
   PubMed Web of Science ®Google Scholar
• Dolan , J.W. ; Snyder , L.R. ; Djordjevic , N.M. ; Hill , D.W. ; Saunders , D.L. ; Van Heukelem , L. ; Waeghe , T.J. Simultaneous variation of temperature and gradient steepness for reversed-phase high-performance liquid chromatography method development: I. Application to 14 different samples using computer simulation . J. Chromatogr. A. 1998 , 803 , 1 – 31 .
   PubMed Web of Science ®Google Scholar
• Snyder , L.R. ; Dolan , J.W. Reversed-phase separation of achiral isomers by varying temperature and either gradient time or solvent strength . J. Chromatogr. A. 2000 , 892 , 107 – 121 .
   PubMed Web of Science ®Google Scholar
• Dolan , J.W. ; Snyder , L.R. ; Wolcott , R.G. ; Haber , P. ; Baczek , T. ; Kaliszan , R. ; Sander , L.C. Reversed-phase liquid chromatographic separation of complex samples by optimizing temperature and gradient time: III. Improving the accuracy of computer simulation . J. Chromatogr. A. 1999 , 857 , 41 – 68 .
   PubMed Web of Science ®Google Scholar
• Heinisch , S. ; Puy , G. ; Barrioulet , M.-P. ; Rocca , J.-L. Effect of temperature on the retention of ionizable compounds in reversed-phase liquid chromatography: Application to method development . J. Chromatogr. A. 2006 , 1118 , 234 – 243 .
   PubMedGoogle Scholar
• Jinno , K. ; Yamagami , M. Simultaneous flow rate and temperature programming based on computer-assisted retention prediction for the separation of PTH-amino acids in reversed-phase microcolumn liquid chromatography . Chromatographia 1989 , 27 , 417 – 424 .
   Web of Science ®Google Scholar
• Horvath , Cs. ; Melander , W. ; Molnar , I. Liquid chromatography of ionogenic substances with nonpolar stationary phases. Anal. Chem. 1977, 49, 142–154.
   Web of Science ®Google Scholar
• Lopes-Marques , R.M. ; Schoenmakers , P.J. Modelling retention in reversed-phase liquid chromatography as a function of pH and solvent composition . J. Chromatogr. 1992 , 592 , 157 – 182 .
   Web of Science ®Google Scholar
• Schoenmakers , P.J. ; Tijssen , R. Modelling retention of ionogenic solutes in liquid chromatography as a function of pH for optimization purposes . J. Chromatogr. A. 1993 , 656 , 577 – 590 .
   Web of Science ®Google Scholar
• Roses , M. ; Canals , I. ; Allemann , H. ; Siigur , K. ; Bosch , E. Retention of ionizable compounds on HPLC. 2. Effect of pH, ionic strength, and mobile phase composition on the retention of weak acids . Anal. Chem. 1996 , 68 , 4094 – 4100 .
   PubMed Web of Science ®Google Scholar
• Hardcastle , J.E. ; Jano , I. Determination of dissociation constants of polyprotic acids from chromatographic data . J. Chromatogr. B. 1998 , 717 , 39 – 56 .
   PubMed Web of Science ®Google Scholar
• Roses , M. ; Bosch , E. Influence of mobile phase acid–base equilibria on the chromatographic behaviour of protolytic compounds . J. Chromatogr. A. 2002 , 982 , 1 – 30 .
   PubMed Web of Science ®Google Scholar
• Nikitas , P. ; Pappa-Louisi , A. New equations describing the combined effect of pH and organic modifier concentration on the retention in reversed-phase liquid chromatography . J. Chromatogr. A. 2002 , 971 , 47 – 60 .
   PubMed Web of Science ®Google Scholar
• Schoenmakers , P.J. ; Biliiet , H.A.H. ; de Galan , L. Systematic study of ternary solvent behaviour in reversed-phase liquid chromatography . J. Chromatogr. 1981 , 218 , 261 – 284 .
   Web of Science ®Google Scholar
• Pappa-Louisi , A. ; Nikitas , P. ; Karageorgaki , M. Retention prediction in ternary solvent reversed-phase liquid chromatography systems based on the variation of retention with binary mobile phase composition . J. Chromatogr. A. 2005 , 1091 , 21 – 31 .
   PubMed Web of Science ®Google Scholar
• Pappa-Louisi , A. ; Nikitas , P. ; Papageorgiou , A. Optimisation of multilinear gradient elutions in reversed-phase liquid chromatography using ternary solvent mixtures . J. Chromatogr. A. 2007 , 1166 , 126 – 134 .
   PubMed Web of Science ®Google Scholar
• Nikitas , P. ; Pappa-Louisi , A. Retention models for isocratic and gradient elution in reversed-phase liquid chromatography . J. Chromatogr. A , 2009 , 1216 , 1737 – 1755 .
   Google Scholar
• Nikitas , P. ; Pappa-Louisi , A. Comments on the two-dimensional smoothing of data . Anal. Chim. Acta. 2000 , 415 , 117 – 125 .
   Google Scholar
• Nikitas , P. ; Pappa-Louisi , A. New approach to linear gradient elution used for optimisation in reversed-phase liquid chromatography . J. Chromatogr. A. 2005 , 1068 , 279 – 287 .
   PubMedGoogle Scholar
• Nikitas , P. ; Pappa-Louisi , A. ; Agrafiotou , P. Multilinear gradient elution optimisation in reversed-phase liquid chromatography using genetic algorithms . J. Chromatogr. A. 2006 , 1120 , 299 – 307 .
   PubMed Web of Science ®Google Scholar
• Nikitas , P. ; Pappa-Louisi , A. ; Papageorgiou , A. Simple algorithms for fitting and optimisation for multilinear gradient elution in reversed-phase liquid chromatography . J. Chromatogr. A. 2007 , 1157 , 178 – 186 .
   PubMed Web of Science ®Google Scholar
• Martinez-Pontevedra , J.A. ; Pensado , L. ; Casais , M.C. ; Cela , R. Automated off-line optimisation of programmed elutions in reversed-phase high-performance liquid chromatography using ternary solvent mixtures . Anal. Chim. Acta. 2004 , 515 , 127 – 141 .
   Web of Science ®Google Scholar
• Cela , R. ; Barroso , C.G. ; Viseras , C. ; Perez-Bustamante , J. A. The PREOPT package for pre-optimization of gradient elutions in high-performance liquid chromatography. Anal. Chim. Acta. 1986, 191, 283–297.
   Google Scholar
• Pappa-Louisi , A. ; Nikitas , P. ; Agrafiotou , P. ; Papageorgiou , A. Optimization of separation and detection of 6-aminoquinolyl derivatives of amino acids by using reversed-phase liquid chromatography with on line UV, fluorescence and electrochemical detection . Anal. Chim. Acta. 2007 , 593 , 92 – 97 .
   PubMedGoogle Scholar
• Nikitas , P. ; Pappa-Louisi , A. ; Papachristos , K. Optimisation technique for stepwise gradient elution in reversed-phase liquid chromatography . J. Chromatogr. A. 2004 , 1033 , 283 – 289 .
   PubMed Web of Science ®Google Scholar
• Dolan , J.W. Temperature selectivity in reversed-phase high performance liquid chromatography . J. Chromatogr. A. 2002 , 965 , 195 – 205 .
   PubMedGoogle Scholar
• Glajch , G.L ; Quarry , M.A. ; Vasta , J.F. ; Snyder , L.R. Separation of peptide mixtures by reversed-phase gradient elution - use of flow-rate changes for controlling band spacing and improving resolution . Anal. Chem. 1986 , 58 , 280 – 285 .
   Web of Science ®Google Scholar
• Li , X.-F. ; Ma , M. ; Cheng , A. ; Zheng , J. ; Tam , Y.K. Determination of testosterone and its metabolites using liquid chromatography with elevated column temperature and flow-rate gradient . Anal. Chim. Acta. 2002 , 457 , 165 – 171 .
   Web of Science ®Google Scholar
• He , Y. ; Lee , H.K. Mobile phase flow programming in liquid chromatography using short narrow bore columns . J. Liq. Chromatogr. Relat. Technol. 1997 , 20 , 2031 – 2039 .
   Web of Science ®Google Scholar
• Sommerburg , O. ; Zang , L.-Y. ; Van Kuijk , F.J.G.M. Simultaneous detection of carotenoids and vitamin E in human plasma . J. Chromatogr. B. 1997 , 695 , 209 – 215 .
   Google Scholar
• Plockova , J. ; Chmelik , J. Different elution modes and field programming in gravitational field-flow fractionation: III. Field programming by flow-rate gradient generated by a programmable pump . J. Chromatogr. A. 2001 , 918 , 361 – 371 .
   PubMed Web of Science ®Google Scholar
• Lesins , V. ; Ruckenstein , E. Gradient flow programming: a coupling of gradient elution and flow programming . J. Chromatogr. 1989 , 467 , 1 – 14 .
   Google Scholar
• Hsieh , Y. ; Wang , G. ; Wang , Y. ; Chackalamannil , S. ; Korfmacher , W.A. Direct plasma analysis of drug compounds using monolithic column liquid chromatography and tandem mass spectrometry . Anal. Chem. 2003 , 75 , 1812 – 1818 .
   PubMed Web of Science ®Google Scholar
• Paci , A. ; Caire-Maurisier , A.-M. ; Rieutord , A. ; Brion , F. ; Clair , P. Dual-mode gradient HPLC procedure for the simultaneous determination of chloroquine and proguanil . J. Pharm. Biomed. Anal. 2002 , 27 , 1 – 7 .
   PubMed Web of Science ®Google Scholar
• Yokoyama , Y. ; Ozaki , O. ; Sato , H. Separation and determination of amino acids, creatinine, bioactive amines and nucleic acid bases by dual-mode gradient ion-pair chromatography . J. Chromatogr. A. 1996 , 739 , 333 – 342 .
   PubMed Web of Science ®Google Scholar
• Earley , R.L. ; Miller , J.S. ; Welch , L.E. The application of flow programming with pulsed amperometric detection for liquid chromatography . Talanta 1998 , 45 , 1255 – 1266 .
   Google Scholar
• Warner , B.D. ; Boehme , G. ; Legg , J.I. Construction and evaluation of a programmable gradient liquid chromatograph. J. Chromatogr. 1981, 210, 419–431.
   Google Scholar
• Kim , W.-S. ; Lee , J.Y. ; Lee , S.K. ; Park , Y.H. ; Lee , D.W. Investigation of retention behavior for herbicides in micro-HPLC with temperature changes . J. Liq. Chromatogr. Relat. Technol. 2003 , 26 , 3357 – 3369 .
   Web of Science ®Google Scholar
• Houdiere , F. ; Fowler , P.W.J. ; Djordjevic , N.M. Combination of column temperature gradient and mobile phase flow gradient in microcolumn and capillary column high-performance liquid chromatography . Anal. Chem. 1997 , 69 , 2589 – 2593 .
   PubMed Web of Science ®Google Scholar
• Moore , L.K. ; Synovec , R.E. Axial thermal gradient microbore liquid chromatography by flow programming . Anal. Chem. 1993 , 65 , 2663 – 2670 .
   Web of Science ®Google Scholar
• Kaliszan , R. ; Wiczling , P. ; Markuszewski , M.J. pH Gradient Reversed-Phase HPLC . Anal. Chem. 2004 , 76 , 749 – 760 .
   PubMedGoogle Scholar
• Kaliszan , R. ; Wiczling , P. ; Markuszewski , M.J. pH gradient high-performance liquid chromatography: theory and applications . J. Chromatogr. A. 2004 , 1060 , 165 – 175 .
   PubMed Web of Science ®Google Scholar
• Kaliszan , R. ; Wiczling , P. Theoretical opportunities and actual limitations of pH gradient HPLC . Anal. Bioanal. Chem. 2005 , 382 , 718 – 727 .
   PubMedGoogle Scholar
• Wiczling , P. ; Kawczak , P. ; Nasal , A. ; Kaliszan , R. Simultaneous determination of pka and lipophilicity by gradient RP HPLC . Anal. Chem. 2006 , 78 , 239 – 249 .
   PubMed Web of Science ®Google Scholar
• Wiczling , P. ; Markuszewski , M.J. ; Kaliszan , M. ; Kaliszan , R. pH/organic solvent double-gradient reversed-phase HPLC . Anal. Chem. 2005 , 77 , 449 – 458 .
   PubMedGoogle Scholar
• Baczek , T. ; Walijewski , Ł. ; Kaliszan , R. pH gradient reversed-phase liquid chromatography as a fractionation tool for the separation of peptides . Talanta 2008 , 75 , 76 – 82 .
   Google Scholar
• Pappa-Louisi , A. ; Nikitas , P. ; Papachristos , K. ; Balkatzopoulou , P. Multi-mode gradient elution in reversed-phase liquid chromatography: Application to retention prediction and separation optimization of a set of amino acids in gradient runs involving simultaneous variations of mobile-phase composition, flow rate and temperature . Anul. Chem. 2009 , 81 , 1217 – 1233 .
   PubMed Web of Science ®Google Scholar
• Pappa-Louisi , A. ; Nikitas , P. ; Agrafiotou , P. Column equilibration effects in gradient elution in reversed-phase liquid chromatography . J. Chromatogr. A. 2006 , 1127 , 97 – 107 .
   PubMed Web of Science ®Google Scholar
• Torres-Lapasio , J.R. ; Roses , M. ; Bosch , E. ; Garcιa-Alvarez-Coque , M.C. Interpretive optimisation strategy applied to the isocratic separation of phenols by reversed-phase liquid chromatography with acetonitrile-water and methanol-water mobile phases . J. Chromatogr. A. 2000 , 886 , 31 – 46 .
   PubMed Web of Science ®Google Scholar
• Pappa-Louisi , A. ; Nikitas , P. Statistical tests for the selection of the optimum parameters set in models describing response surfaces in reversed-phase liquid chromatography . Chromatographia 2003 , 57 , 169 – 176 .
   Google Scholar
• Levenberg , K. A method for the solution of certain problems in least squares . Quart. Appl. Math. 1944 , 2 , 164 – 168 .
   Google Scholar
• Marquardt , D. An algorithm for least-squares estimation of nonlinear parameters. SIAM J. Appl. Math. 1963, 11, 431–441.
   Web of Science ®Google Scholar
• Press , W.H. ; Teukolsky , S.A. ; Vetterling , W.T. ; Flannery , B.P. In Numerical Recipes in C , , 2nd Ed. ; Cambridge University Press : Cambridge , 1992 .
   Google Scholar
• Nikitas , P. ; Pappa-Louisi , A. Non-linear least-squares fitting with microsoft excel solver and related routines in HPLC modelling of retention. I. Considerations of the problems of the method . Chromatographia 2000 , 52 , 477 – 486 .
   Google Scholar
• Michalewicz , Z. Genetic algorithms + data structures = Evolution Programs ; Springer : Berlin , 1996 .
   Google Scholar
• Goldberg , D.E. Genetic Algorithms in Search, Optimization and Machine Learning ; Addison-Wesley : Reading , 1989 .
   Google Scholar
• Pham , D.T. ; Karaboga , D. Intelligent Optomisation Techniques ; Springer : Berlin , 2000 .
   Google Scholar
• Nikitas , P. ; Pappa-Louisi , A. ; Papageorgiou , A. ; Zitrou , A. On the use of genetic algorithms for response surface modeling in high-performance liquid chromatography and their combination with the Microsoft Solver . J. Chromatogr. A. 2002 , 942 , 93 – 105 .
   PubMed Web of Science ®Google Scholar
• Nikitas , P. ; Papageorgiou , A. Modifications of the classical genetic algorithm for non-linear fitting applied to response surface modeling in HPLC . Comput. Phys. Commun. 2001 , 141 , 225 – 229 .
   Google Scholar
• Cela , R. ; Martinez , J.A. ; Gonzalez-Barreiro , C. ; Lores , M. Multi-objective optimisation using evolutionary algorithms: its application to HPLC separations . Chemometrics Intell. Lab. Syst. 2003 , 69 , 137 – 156 .
   Web of Science ®Google Scholar
• Berridge , J.C. Techniques for the automated Optimization of HPLC Separations ; Wiley : Chichester , 1985 ; 137 .
   Google Scholar
• Smilde , A.K. ; Knevelman , A. ; Coenegracht , P.M.J. Introduction of multi-criteria decision making in optimization procedures for high-performance liquid chromatographic separations . J. Chromatogr. 1986 , 369 , 1 – 10 .
   Web of Science ®Google Scholar
• Keller , H.R. ; Massart , D.L. Program for Pareto-optimality in multicriteria problems . Trends Anal. Chem. 1990 , 9 , 251 – 253 .
   Google Scholar
• Sáiz-Abajo , M.J. ; González-Sáiz , J.M. ; Pizarro , C. Multi-objective optimisation strategy based on desirability functions used for chromatographic separation and quantification of -proline and organic acids in vinegar . Anal. Chim. Acta. 2005 , 528 , 63 – 76 .
   Google Scholar
• Hadjmohammadi , M.R. ; Safa , F. Multi-criteria decision making in micellar liquid chromatographic separation of chlorophenols . J. Sep. Sci. 2004 , 27 , 997 – 1004 .
   PubMed Web of Science ®Google Scholar
• Derringer , G. ; Suich , R. Simultaneous optimization of several response variables . J. Qual. Technol. 1980 , 12 , 214 – 219 .
   Web of Science ®Google Scholar
• Bourguignon , B. ; Massart , D.L. UNIFAC model as a heuristic guide for estimating retention in chromatography . J. Chromatogr. 1991 , 586 , 1 – 9 .
   Google Scholar
• Safa , F. ; Hadjmohammadi , M.R. Simultaneous optimization of the resolution and analysis time in micellar liquid chromatography of phenyl thiohydantoin amino acids using Derringer's desirability function . J. Chromatogr. A. 2005 , 1078 , 42 – 50 .
   PubMed Web of Science ®Google Scholar
• Glajch , J.L. ; Kirkland , J.J. Method development in high-performance liquid chromatography using retention mapping and experimental design techniques. J. Chromatogr. 1989, 485, 51–63.
   Web of Science ®Google Scholar